Math Problem Statement
The table below gives the annual sales (in millions) of a product.
year
1998
1999
2000
2001
2002
2003
2004
2005
2006
sales
297
351
393
423
441
447
441
423
393
What was the average rate of change of annual sales
a) Between 2002 and 2003
16 millions of dollars/year
b) Between 2002 and 2004
millions of dollars/year
Solution
To find the average rate of change of annual sales, we use the formula for the average rate of change between two points:
Part (a): Average Rate of Change Between 2002 and 2003
- Sales in 2002: 441 million dollars
- Sales in 2003: 447 million dollars
Change in sales:
Change in time:
Average rate of change:
So, the average rate of change of annual sales between 2002 and 2003 is 6 million dollars/year.
Part (b): Average Rate of Change Between 2002 and 2004
- Sales in 2002: 441 million dollars
- Sales in 2004: 441 million dollars
Change in sales:
Change in time:
Average rate of change:
So, the average rate of change of annual sales between 2002 and 2004 is 0 million dollars/year.
Would you like any more details or have any other questions?
Here are some related questions you might find interesting:
- What is the total change in sales from 1998 to 2006?
- How do you interpret the negative rate of change in sales after 2003?
- What is the overall trend in sales from 1998 to 2006?
- How would you model this sales data with a polynomial function?
- What is the maximum sales value, and in what year does it occur?
Tip: The average rate of change is a useful way to understand how a quantity is changing over time, similar to the concept of slope in algebra.
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Math Problem Analysis
Mathematical Concepts
Average Rate of Change
Formulas
Average rate of change formula: Change in sales / Change in time
Theorems
-
Suitable Grade Level
Grades 9-12
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